Depends entirely on the on-call rotation. I've been on one where you could go the entire week without being paged, and where most of the pages did not require an immediate response. That did not prevent me from living my life. I've been on another where there were several pages every day, at all hours of the day, each of which could take anywhere from 30 minutes to several hours. That one certainly prevented me from living my life.
How does an on-call rotation prevent this?